Imaging of a scattering medium relates generally to a modality for generating an image of the spatial distribution of properties (such as the absorption or scattering coefficients) inside a scattering medium through the introduction of energy into the medium and the detection of the scattered energy emerging from the medium. Systems and methods of this type are in contrast to projection imaging systems, such as x-ray. X-ray systems, for example, measure and image the attenuation or absorption of energy traveling a straight line path between the x-ray energy source and a detector, and not scattered energy. Whether energy is primarily highly scattered or primarily travels a straight line path is a function of the wavelength of the energy and medium it is traveling through.
Imaging based on scattering techniques permits the use of new energy wavelengths for imaging features of the human body, earth strata, atmosphere and the like that can not be imaged using projection techniques and wavelengths. For example, x-ray projection techniques may be adept at imaging bone structure and other dense objects, but are relatively ineffective at distinguishing and imaging blood oxygenation levels. This is because the absorption coefficient of blood does not vary significantly with blood oxygenation, at x-ray wavelengths. However, infrared energy can identify the spatial variations in blood volume and blood oxygenation levels because the absorption coefficient at these wavelengths is a function of hemoglobin states. Other structures and functions can be identified by variations or changes in the scattering coefficient of tissue exposed to infrared energy, such as muscle tissue during contraction, and nerves during activation. These structures could not be imaged by projection techniques because projection techniques are not effective in measuring variations in scattering coefficients. These measures, obtainable through imaging based on scattering techniques, such as optical tomography, have considerable potential value in diagnosing a broad range of disease processes.
A typical system for imaging based on scattered energy measures, includes at least one energy source for illuminating the medium and at least one detector for detecting emerging energy. The energy source is selected so that it is highly scattering in the medium to be imaged. The source directs the energy into the target scattering medium and the detectors on the surface of the medium measure the scattered energy as it exits. Based on these measurements, a reconstructed image of the internal properties of the medium is generated.
The reconstruction is typically carried out using “perturbation methods.” These methods essentially compare the measurements obtained from the target scattering medium to a known reference scattering medium. The reference medium may be a physical or a fictitious medium which is selected so that it has properties that areas close as possible to those of the medium to be imaged. Selecting a reference medium is essentially an initial guess of the properties of the target. In the first step of reconstruction, a “forward model” is used to predict what the detector readings would be for a particular source location based on the known internal properties of the reference medium. The forward model is based on the transport equation or its approximation, the diffusion equation, which describes the propagation of photons through a scattering medium. Next, a perturbation formulation of the transport equation is used to relate (1) the difference between the measured and predicted detector readings from the target and reference, respectively, to (2) a difference between the unknown and known internal properties of the target and reference, respectively. This relationship is solved for the unknown scattering and absorption properties of the target. The final distributions of internal properties are then displayed or printed as an image.
Imaging systems and methods based on scattering techniques, such as optical tomography systems, provide a means with which to examine and image the internal properties of scattering media, such as the absorption and diffusion or scattering coefficients. However, the aforementioned imaging systems and methods that recover, contrast features of dense scattering media have thus far produced results having at best modest spatial resolution. Strategies for improving image quality are known (e.g., Newton type), but invariably these are computationally intensive and can be quite sensitive to initial starting conditions.
Central to the method of image formation in magnetic resonance imaging (MRI) is that there is a one-to-one correspondence between the frequency of the measured induced current and the spatial orientation of the magnetic field gradient. Because the spatial orientation of the magnetic field gradient is known, this correspondence permits a direct assignment of a measured response to the origin of the signal in space. In effect, the physics of the magnetic resonance phenomenon encodes a frequency signature into the measured data that has a known spatial relationship with the target medium. More generally speaking, methods of this type are known as “frequency encoded spatial filtering.”
For the foregoing reasons, there is a need for a computationally efficient nonlinear correction method that is capable of significantly improving the quality of solutions to a system of linear equations such as reconstructed images of a scattering medium.